2D Vector Calculator
Add, subtract, and compute the dot product, cross product magnitude, and angle between two 2D vectors.
Vector Results
2D Vector Operations for vectors A = (Ax, Ay) and B = (Bx, By):
Addition: A + B = (Ax + Bx, Ay + By)
Subtraction: A − B = (Ax − Bx, Ay − By)
Dot Product: A · B = Ax×Bx + Ay×By
Cross Product Magnitude (2D): |A × B| = Ax×By − Ay×Bx
This is the z-component of the 3D cross product and equals the area of the parallelogram formed by the two vectors.
Angle Between:
θ = arccos((A · B) / (|A| × |B|))
Magnitude: |A| = √(Ax² + Ay²)